Express the following as a sum or difference 1) 2sin54.sin66 2) 2sin54.cos66
Answers
Answer:
Cos(12) - Cos120 = 2sin54.sin66
Sin(120) - Sin12 = 2sin54.cos66
Step-by-step explanation:
Express the following as a sum or difference 1) 2sin54.sin66 2) 2sin54.cos66
2sin54.sin66
Cos(A-B) - Cos(A+B) = 2SinASinB
=> Cos(54 - 66) - Cos(54 + 66) = 2sin54.sin66
=> Cos(-12) - Cos(120) = 2sin54.sin66
=> Cos(12) - Cos120 = 2sin54.sin66
Sin(A+B) + Sin(A-B) = 2SinACosB
=> Sin(54 + 66) + Sin(54 - 66) = 2sin54.cos66
=> Sin(120) + SIn(-12) = 2sin54.cos66
=>Sin(120) - Sin12 = 2sin54.cos66
Additional info
2sin54.sin66
= 2 Sin(60 -6)Sin(60 + 6)
Using Sin ( A + B) = SinAcosB + CosA SinB
& Sin ( A - B) = SinAcosB - CosA SinB
= 2(Sin60Cos6 - Cos60Sin6)(Sin60Cos6 + Cos60Sin6)
= 2(Sin²60Cos²6 - Cos²60Sin²6)
= 2(3Cos²6/4 - Sin²6/4)
= (1/2)( 3Cos²6 - Sin²6)
= (1/2)(4Cos²6 - 1)
Answer:
(ii) 2 sin 54° sin 66°
=√3/2- sin12
Step-by-step explanation:
2 cos 54 . sin 66
=sin (66+54)+sin(66-54)
=sin 120 - sin 12
=√3/2+ sin12